On vertex coloring of graphs

Abstract

The concept of vertex coloring pose a number of challenging open problems in graph theory. Among several interesting parameters, the coloring parameter, namely the pseudoachromatic number of a graph stands a class apart. Although not studied very widely like other parameters in the graph coloring literature, it has started gaining prominence in recent years. The pseudoachromatic number of a simple graph G, denoted ψ(G), is the maximum number of colors used in a vertex coloring of G, where the adjacent vertices may or may not receive the same color but any two distinct pair of colors are represented by at least one edge in it. In this paper we have computed this parameter for a number of classes of graphs.

Suitable Site Selection of Water ATMs (Basis of Interior/Exterior Conditions) Using Graph Theory

“…The key result t PMC 2 (G) = tMM * 2 (G) = g(k − 1) − 1 with some suitable conditions is obtained, where g is the girth of G. Tsalouchidou et al (2020) calculated the bi-objective notion of shortest-fastest path (SFP) in temporal graphs, which studies both space and time as a linear mixture governed by a parameter. Yegnanarayanan et al (2015) calculated the pseudo a chromatic number of a simple graph G, denoted ψ(G), is the concentrated number of colors used in a vertex coloring of G, where the adjacent vertices may or may not obtain the identical color but any two separate pair of colors are signified by at least one edge in it. They have planned this parameter for a number of classes of graphs.…”